Roughly how long do your open strings carry on "ringing" after you have come off a short staccato note? Is there a good way of deadening them earlier if you feel it's marring a technical passage? I find my open G on my viola will happily sound for several seconds and that I don't feel the technical passages with string crossings sound very 'clean' because there is this ringing G in the background. I recorded myself and it's not nearly as noticeable on the recording as it is to me while playing, but still curious if I can use any particular type of technique or bowing to make it shut up!

Ah this is interesting. I was an advanced classical guitarist before taking up violin, and if you want to play well on guitar you have to do all sorts of damping of the strings to keep things clean, with both hands. To be honest I do it automatically on violin because of my guitar hangover, just lightly touching any string that's making an unwanted noise. I don't think my violin teacher has noticed me doing it and I do it without thinking so haven't mentioned it. Guitarists have more obvious ringing-on to control, but it's still an issue with orchestral strings. I wonder what cellists/double bassists do, it must be more obvious for them.